## Search found 776 matches

- Thu May 16, 2019 10:39 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Refuting Gödel's 1931 Incompleteness Theorem in one sentence
- Replies:
**121** - Views:
**2080**

### Re: Refuting Gödel's 1931 Incompleteness Theorem in one sentence

We could for example provide an cancer doctor that is all knowing about cancer. This machine would have the sum total of all human general knowledge immediately available for any purpose. Isn't that just the failed idea of expert systems straight out of 1980? Correction. 1965. https://en.wikipedia....

- Thu May 16, 2019 12:12 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Does anyone here actually understand formal proofs of mathematical logic?
- Replies:
**122** - Views:
**1979**

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Hilbert's failed dream.PeteOlcott wrote: ↑Thu May 16, 2019 12:07 amAND the Sound deductive inference model proves this is impossible.

In the Sound deductive inference model True is ONLY PROVABLE TRUE,

thus NOT PROVABLE IS NOT TRUE.

https://en.wikipedia.org/wiki/Hilbert%27s_program

Wir müssen wissen.

Wir werden wissen.

- Sun May 12, 2019 12:13 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

Instead of looking for such an Integer in the Axiom of Choice ... That's pathetically incoherent. The concept that it is fruitless to look for an integer that is both greater than and less than 5 is incoherent? What do you think that would have to do with the axiom of choice? I really want to hear ...

- Sun May 12, 2019 12:09 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

That's pathetically incoherent.PeteOlcott wrote: ↑Sat May 11, 2019 11:57 pmInstead of looking for such an Integer in the Axiom of Choice ...

- Sat May 11, 2019 11:20 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

All the best brother.

- Sat May 11, 2019 10:35 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

See https://en.wikipedia.org/wiki/Non-well- ... set_theoryPeteOlcott wrote: ↑Sat May 11, 2019 4:23 pmno physical or

conceptual thing can ever totally contain itself.

PeteOlcott wrote: ↑Sat May 11, 2019 5:55 pmCounter-examples to stipulated definitions are not allowed.

Are you honestly under the impression that this is a coherent response to what I wrote?

- Sat May 11, 2019 9:45 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

I'd like to make some comments on your reply. I don't feel that I"m arguing a position, so you don't need to snap back at each point. I'm just outlining some of the obvious objections that: 1) Will be asked by ANYONE you present your ideas to; 2) And that in my opinion, you haven't handled very well...

- Fri May 10, 2019 11:01 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

There cannot possibly be a counter-example to my thesis I presented one. Several times. But if you don't think the axiom of choice is a counterexample, just tell me whether it's true or false. You'd become famous if you could answer that question. But you can't even be bothered to look it up on Wik...

- Fri May 10, 2019 10:26 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

I am not going to bother to learn every detail of all of mathematics to prove a single point. What you call a "detail" is in fact a counterexample to your thesis. That you can't be bothered to engage with it shows you're not serious. The axiom of choice is the CLASSIC EXAMPLE of a closed wff that i...

- Fri May 10, 2019 5:51 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

That question was absurd. I don't answer those. The question was perfectly sensible. I asked you about the consequences of redefining material implication to be logical conjunction. So that "2 + 2 = 4 AND Washington is regarded as the father of his country" is the same truth connective as "2 + 2 = ...

- Fri May 10, 2019 3:33 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

Avoiding the question I asked?PeteOlcott wrote: ↑Fri May 10, 2019 2:11 amIt sure as Hell makes much more sense than saying that every truth is logically

entailed by either falsehood or contradiction.

- Fri May 10, 2019 12:13 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

I would correct it to conform to the English meaning this way: Logical implication p q p ⇒ q T T T T F F F T F F F F Isn't that what everyone else calls logical AND? Would you say that * 2 + 2 = 4 and George Washington is regarded as the father of his country. and * 2 + 2 = 4 THEREFORE George Washi...

- Wed May 08, 2019 12:47 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2419**

### Re: Possible consequences of falsifying the principle of explosion?

Instead of undecidable logic sentences "proving" incompleteness of formal systems they are merely rejected as derived from unsound deduction. That doesn't make any sense. If a sufficiently interesting system is consistent, it must necessarily contain closed wffs that can neither be proven nor dispr...

- Sat May 04, 2019 7:38 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1683**

### Re: Converting formal proofs to conform to sound deduction

Copyright ???? Pete Olcott It's not a legal copyright without a year. When I was a tech writer (a very long time ago) I learned to write "Copyright (C) 1920 Thomas Edison Company" in exactly that format. Just some free legal advice. And of course I'm not a lawyer and the law might have changed sinc...

- Fri May 03, 2019 4:23 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1683**

### Re: Converting formal proofs to conform to sound deduction

mortal adjective of a living human being often in contrast to a divine being subject to death. Thanks for clarifying your thinking. You are making the point that under your understanding of logic, we should analyze the word "mortal" and so forth. I'd submit that if you show the phrase "All men are ...